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The continuous time system described by 2 y(t) = x (t2) is
- a)Causal, linear and time varying
- b)Causal, non-linear and time varying
- c)Non causal, non-linear and time-invariant
- d)Non causal, linear and time-invariant
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The continuous time system described by 2 y(t) = x (t2) isa)Causal, li...
Explanation: Y (t) depends upon the future value therefore the system is anticipative and hence is not causal. But as it follows the superposition theorem so it is linear.
Most Upvoted Answer
The continuous time system described by 2 y(t) = x (t2) isa)Causal, li...
Explanation:
To determine the causality, linearity, and time invariance of the given system, we need to analyze its properties based on the given equation.
Causality:
A system is causal if its output at any given time depends only on the present and past values of the input. In the given equation, the output y(t) is dependent on the input x(t^2). Since the input signal is squared, it implies that the output depends on the past values of the input. Therefore, the system is causal.
Linearity:
A system is linear if it follows the principles of superposition and homogeneity. Superposition states that the output due to the sum of two inputs is equal to the sum of the outputs due to each input individually. Homogeneity states that scaling the input will cause the output to scale accordingly. In the given equation, we have 2y(t) = x(t^2). By applying a constant factor to the input, the output will also scale by the same factor (2). Additionally, if we have two inputs, x1(t^2) and x2(t^2), the output will be 2y1(t) + 2y2(t) = 2(x1(t^2) + x2(t^2)), satisfying the principle of superposition. Therefore, the system is linear.
Time Invariance:
A system is time-invariant if a time shift in the input signal results in the same time shift in the output signal. In the given equation, we can observe that there is no explicit time shift or delay introduced in the input or output signals. Therefore, the system is time-invariant.
Conclusion:
Based on the analysis, the given system is causal, linear, and time-invariant, which corresponds to option 'D'.
To determine the causality, linearity, and time invariance of the given system, we need to analyze its properties based on the given equation.
Causality:
A system is causal if its output at any given time depends only on the present and past values of the input. In the given equation, the output y(t) is dependent on the input x(t^2). Since the input signal is squared, it implies that the output depends on the past values of the input. Therefore, the system is causal.
Linearity:
A system is linear if it follows the principles of superposition and homogeneity. Superposition states that the output due to the sum of two inputs is equal to the sum of the outputs due to each input individually. Homogeneity states that scaling the input will cause the output to scale accordingly. In the given equation, we have 2y(t) = x(t^2). By applying a constant factor to the input, the output will also scale by the same factor (2). Additionally, if we have two inputs, x1(t^2) and x2(t^2), the output will be 2y1(t) + 2y2(t) = 2(x1(t^2) + x2(t^2)), satisfying the principle of superposition. Therefore, the system is linear.
Time Invariance:
A system is time-invariant if a time shift in the input signal results in the same time shift in the output signal. In the given equation, we can observe that there is no explicit time shift or delay introduced in the input or output signals. Therefore, the system is time-invariant.
Conclusion:
Based on the analysis, the given system is causal, linear, and time-invariant, which corresponds to option 'D'.
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The continuous time system described by 2 y(t) = x (t2) isa)Causal, linear and time varyingb)Causal, non-linear and time varyingc)Non causal, non-linear and time-invariantd)Non causal, linear and time-invariantCorrect answer is option 'D'. Can you explain this answer?
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